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Answer :
To solve this problem, let's break it down step by step:
We're dealing with an isosceles triangle, which means it has two sides of equal length and one side that is different. Given the information, the perimeter of the triangle is 7.5 meters, and the shortest side, [tex]\( y \)[/tex], is 2.1 meters.
We need to find a suitable equation from the given options that will help us determine the value of [tex]\( x \)[/tex], the length of the other two equal sides.
1. Identify Components:
- The perimeter of a triangle is the sum of the lengths of all its sides. For an isosceles triangle, the formula for the perimeter is [tex]\( 2x + y \)[/tex], where [tex]\( x \)[/tex] is the length of the equal sides.
- We're given [tex]\( y = 2.1 \)[/tex] meters and the perimeter = 7.5 meters.
2. Set Up the Equation:
- Use the perimeter formula: [tex]\( 2x + y = 7.5 \)[/tex].
- Substitute [tex]\( y = 2.1 \)[/tex] into the equation: [tex]\( 2x + 2.1 = 7.5 \)[/tex].
3. Solve for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Now, we need to find which given equation equates correctly using the computed value of [tex]\( x = 2.7 \)[/tex].
Let's check the given options:
- [tex]\( 2x - 2.1 = 7.5 \)[/tex] - This leads to incorrect results because it doesn't account for the correct equation form.
- [tex]\( 4.2 + y = 7.5 \)[/tex] - This setup doesn't match our perimeter structure.
- [tex]\( y - 4.2 = 7.5 \)[/tex] - This is again not applicable for the perimeter calculation.
- [tex]\( 2.1 + 2x = 7.5 \)[/tex] - This matches the equation we derived!
Thus, the correct equation is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
We're dealing with an isosceles triangle, which means it has two sides of equal length and one side that is different. Given the information, the perimeter of the triangle is 7.5 meters, and the shortest side, [tex]\( y \)[/tex], is 2.1 meters.
We need to find a suitable equation from the given options that will help us determine the value of [tex]\( x \)[/tex], the length of the other two equal sides.
1. Identify Components:
- The perimeter of a triangle is the sum of the lengths of all its sides. For an isosceles triangle, the formula for the perimeter is [tex]\( 2x + y \)[/tex], where [tex]\( x \)[/tex] is the length of the equal sides.
- We're given [tex]\( y = 2.1 \)[/tex] meters and the perimeter = 7.5 meters.
2. Set Up the Equation:
- Use the perimeter formula: [tex]\( 2x + y = 7.5 \)[/tex].
- Substitute [tex]\( y = 2.1 \)[/tex] into the equation: [tex]\( 2x + 2.1 = 7.5 \)[/tex].
3. Solve for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Now, we need to find which given equation equates correctly using the computed value of [tex]\( x = 2.7 \)[/tex].
Let's check the given options:
- [tex]\( 2x - 2.1 = 7.5 \)[/tex] - This leads to incorrect results because it doesn't account for the correct equation form.
- [tex]\( 4.2 + y = 7.5 \)[/tex] - This setup doesn't match our perimeter structure.
- [tex]\( y - 4.2 = 7.5 \)[/tex] - This is again not applicable for the perimeter calculation.
- [tex]\( 2.1 + 2x = 7.5 \)[/tex] - This matches the equation we derived!
Thus, the correct equation is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
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